Noncommuting Graph

The noncommuting graph of a non-Abelian group is the simple graph with vertex set $G\Z(G)$ in which two vertices are adjacent precisely when they do not commute. Here is the group center. Its clique number is the largest size of a pairwise noncommuting set in , and its chromatic number is the least size of an Abelian cover of (Lecomte 2026).

See also

Abelian Cover, Abelian Group, Chromatic Number, Clique Number, Group Center

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References

Lecomte, G. "Eventual Exactness and Rigidity for Abelian Covers of Groups." 12 Oct 2026. https://arxiv.org/abs/2610.22388.

Cite this as:

Weisstein, Eric W. "Noncommuting Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NoncommutingGraph.html

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